Log-transform and the weak Harnack inequality for kinetic Fokker-Planck equations
Analysis of PDEs
2021-02-09 v1
Abstract
This article deals with kinetic Fokker-Planck equations with essentially bounded coefficients. A weak Harnack inequality for non-negative super-solutions is derived by considering their Log-transform and following S. N. Kruzhkov (1963). Such a result rests on a new weak Poincar{\'e} inequality sharing similarities with the one introduced by W. Wang and L. Zhang in a series of works about ultraparabolic equations (2009, 2011, 2017). This functional inequality is combined with a classical covering argument recently adapted by L. Silvestre and the second author (2020) to kinetic equations.
Keywords
Cite
@article{arxiv.2102.04105,
title = {Log-transform and the weak Harnack inequality for kinetic Fokker-Planck equations},
author = {Jessica Guerand and Cyril Imbert},
journal= {arXiv preprint arXiv:2102.04105},
year = {2021}
}